System And Methods For Modeling Consequences Of Events

ABSTRACT

Methods, systems, and computer program products are provided for modeling consequences of events on performance indicators. A causality model is provided to define relationships between events and the consequences associated with each one of the events to modify a value of at least one of the performance indicators associated with each one of the events. An algorithm included in the causality model is executable to compute an impact of the consequences on the value. A causality model management system is provided to manage the causality model, including storing, execution of the algorithm, interfacing with other systems, and simulating what-if scenarios of the events and the performance indicators.

BACKGROUND OF THE INVENTION

Over the last few years, information technology (IT) organizations haveincreasingly adopted standards and best practices to ensure efficient ITservice delivery. In this context, the IT Infrastructure Library (ITIL)has been rapidly adopted as the de facto standard. ITIL defines a set ofstandard processes for the management of IT service delivery organizedin processes for Service Delivery (Service Level Management, CapacityManagement, Availability Management, IT Continuity Management andFinancial Management) and Service Support (Release Management,Configuration Management, Incident Management, Problem Management andChange Management). The Service Support processes, such as ConfigurationManagement, Incident Management, and Configuration Management are someof the more common processes IT organizations have implemented to bringtheir service to an acceptable level for their businesses.

The implementation of ITIL processes has yielded significant results toIT organizations by defining clear interfaces between service providersand consumers, by clarifying the IT organizational structures, roles,and responsibilities, and by designing internal processes for themanagement of IT operations. However, once ITIL processes areimplemented, the effectiveness of the IT organization depends on theability of the decision makers involved in those processes to maketimely and accurate decisions. Hence, regardless of the quality of theprocess implementation, if inadequate decisions are made during theexecution of those processes, they will result in poor customerexperience and low value delivery. For instance, being able toprioritize a large volume of incidents based on their likely impact onthe IT organization is key to running an efficient Incident Managementprocess.

The challenge facing IT Service Management is to develop decisionsupport capabilities that will enable decision makers to drive theirmanagement processes efficiently. An organizational structure andprocesses referred to as IT Governance can be used to define thestrategy of the IT organization and oversee its execution to achieve thegoals of the enterprise. One of the goals of IT Governance is to deliverIT services in alignment with business objectives. The businessobjectives are used as input to derive goals, objectives, andperformance metrics needed to manage IT effectively. Auditing processesare used to measure and analyze the performance of the organization. Aconcept referred to as the Balanced Scorecard combines financialmeasures and non-financial measures in a single report and has been usedas a strategic and performance measurement tool for IT Governance.However, the development of the balanced scorecard has been focused onthe structural aspects (including design processes, metric selection,and ranking) and on the reporting aspects (including metric collectionand ranking). The further development and use of the balanced scorecardto drive business decisions within an enterprise to align businessstrategy with IT operations has been limited.

SUMMARY

The teachings of the present disclosure relate to methods, systems, andcomputer program products for modeling consequences of events onperformance indicators. Described herein are several methods, systems,and computer program products for developing a causal model capable ofdetermining the consequences of events on performance indicators. Acausality model is provided to define relationships between events andthe consequences associated with each one of the events to modify avalue of at least one of the performance indicators associated with eachone of the events. An algorithm included in the causality model isexecutable to compute an impact of the consequences on the value. Acausality model management system is provided to manage the causalitymodel, including storing, execution of the algorithm, interfacing withother systems, and simulating what-if scenarios of the events and theperformance indicators.

BRIEF DESCRIPTION OF THE DRAWINGS

Embodiments of the invention relating to both structure and method ofoperation may best be understood by referring to the followingdescription and accompanying drawings:

FIG. 1 illustrates an exemplary structure of a generalized balancedscorecard 100, according to an embodiment;

FIG. 2 describes a diagram illustrating a derivation process of autility function having a ‘greater than’ type objective, according to anembodiment;

FIG. 3 is a block diagram of a causality model illustrating a causalrelationship between sets of an alternative, event, performanceindicator, objective and balanced scorecard, according to an embodiment;

FIG. 4 is a graphical illustration of decision alternatives configuredas a set of lotteries, according to an embodiment;

FIG. 5 is a flow chart of a method for decision making underuncertainty, according to an embodiment;

FIG. 6 illustrates an exemplary representation of a causality modeldescribed with reference to FIG. 3 using a unified modeling language(UML), according to an embodiment;

FIG. 7 is a flow chart of a method for modeling consequences of eventson performance indicators, according to an embodiment;

FIG. 8 is a block diagram illustrating a causality model managementsystem, according to an embodiment; and

FIG. 9 illustrates a block diagram of a computer system, according to anembodiment.

DETAILED DESCRIPTION

Applicants recognize that it would be desirable to provide a causalframework that would include tools and techniques to make businessdecisions under uncertainty that would leverage the use of balancedscorecard in selecting alternatives, thereby ensuring alignment betweenbusiness strategy and IT operations, including IT services and ITinfrastructure. That is, it would be desired to provide tools andtechniques that would evaluate various business alternatives under riskin quantifiable terms and assess their impact on the objectivesidentified in the balanced scorecard. Applicants further recognize thatthe selection of a particular alternative from a set of alternatives isa multi criteria decision making (MCDM) problem under uncertainty whencriteria are modeled as objectives in balanced scorecards. Therefore, aneed exists to provide improved tools and techniques to be used indecision support systems for modeling consequences of events onperformance indicators, and hence on balanced scorecards.

The following terminology may be useful in understanding the presentdisclosure. It is to be understood that the terminology described hereinis for the purpose of description and should not be regarded aslimiting.

Framework—A basic structure designed to provide one or more functions. Aframework used in a computer hardware and software environment may betypically designed to include processes to deliver core functions andextensible functions. The core functions are typically a portion of theframework that may not be modifiable by the framework user. Theextensible functions are typically a portion of the framework that hasbeen explicitly designed to be customized and extended by the frameworkuser as a part of the implementation process. For example, ControlObjectives for Business Information-related Technology (COBIT) is a typeof a framework used for addressing the management's need for control andmeasurability of IT services. The framework may also include applicationprogram interfaces that allow an external program to access thefunctions of the framework.

Balanced Scorecard—A collection of key measures (financial andnon-financial) introduced by Robert Kaplan and David Norton that anenterprise may define to measure its performance in executing a strategyand ‘balance’ the business perspective with the IT service perspective.A typical balanced scorecard may include 4 perspectives (a perspectivemay be defined as a group or combination of objectives pertainingtowards a particular function of the business), including financial,customer, business process, and learning/growth perspectives. Ageneralized balanced score card may include a set of n perspectives.

Key performance indicator (KPI) (or simply a performance indicator)—KPIis an actionable metric. As defined by COBIT, KPI's are measurableindicators of performance of the enabling factors of IT processes,indicating how well the process enables the goal to be reached.

Objectives—Measurable indicators of the business objectives. Theobjectives typically express one or more target values over a KPI.

Lottery—A lottery is a type of gaming process that awards prizes basedon the element of probability or chance. If Z is a finite set ofconsequences (or prizes or outcomes), then a lottery is a probabilitydistribution on Z.

System—One or more interdependent elements, components, modules, ordevices that co-operate to perform one or more predefined functions.

Configuration—Describes a set up of elements, components, modules,devices, and/or a system, and refers to a process for setting, defining,or selecting hardware and/or software properties, parameters, orattributes associated with the elements, components, modules, devices,and/or the system.

Systems and methods disclosed herein provide an open model forexpressing declaratively causal relationships between IT events andperformance indicators. The model is said to be open because theframework provides for different styles of consequences to be expressedthrough the concept of “modifier”. A modifier can be a probabilitydistribution expressed over a range of key performance indicators(KPI's). Therefore, a consequence expresses how events are likely tomodify the values of KPI's.

Management of Information Technology Infrastructure Library (ITIL)processes can be based on objectives defined in balanced scorecards tohelp ensure that IT management decisions and processes are aligned withbusiness objectives. In terms of decision theory, criteria modeled asbalanced scorecard objectives presents a multi-criteria decision making(MCDM) problem under uncertainty. Cost functions, utility functions orother means to assess or compare alternatives are defined to achieveefficient, business driven prioritization and scheduling. The functionsmeasure the impact of IT management alternatives against the objectivesdefined in a balanced scorecard.

Model for Balanced Scorecard Generalized Scorecard

Given a set A of IT management alternatives, a preference relation overthe element of A is defined based on the relationship betweenalternatives and their impact on scorecard objectives. FIG. 1illustrates an exemplary structure of a generalized balanced scorecard100, according to an embodiment. The generalized balanced scorecard 100may include the following:

-   -   A set of perspectives P={P₁ 110, . . . ,P_(n) 120}    -   A set of related weights Z={ζ₁, . . . , ζ_(n)}; where each        ζ_(j), (1≦i≦n) is the relative weight of the i^(th) perspective        in P and Σ_(i=1) ^(n)ζ_(i)=1    -   An evaluation period Tp        A perspective can be formally defined as:    -   A set of objectives O={O₁ 112, . . . , O_(n) 122}    -   A set of related weights Ω={ω₁, . . . , ω_(n)}: where each        ω_(i), (1≦i≦n) is the relative weight of the i^(th) objective in        O and Σ_(i=1) ^(n)ω₁=1

The set of all available performance indicators (also referred to moregenerally as metrics) K={κ_(i) 114, . . . , κ_(n) 124} and the set ofdomain values D={D₁, . . . , D_(n)} where each D₁, (1≦i≦n) is a finiteset of possible values for performance indicator κ_(i). D will also beused to denote the space of all possible outcomes, which is theCartesian product of D=D₁×D₂× . . . ×Dn.

An objective O_(i), (1≦i≦n) was defined above as a constraint expressedover an element κ_(j) of the set K and an element of its associateddomain value D_(j). Constraints in scorecards admit two comparators,(“below” or “lower than”) and (“above” or “greater than”).

The generalized scorecard model, with a constraint approach to thedefinition of the objective is specifically useful for activities suchas scorecard performance monitoring and reporting. However, for decisionsupport, the definition of an objective as a constraint is too limited.Accordingly, a utilitarian approach to the definition of scorecardobjectives may be taken.

Utilitarian Scorecard

As described in the previous section, a scorecard perspective is a setof objectives over which a preference function is defined. An objectiveis a constraint expressed between a performance indicator and an elementof its domain value. In a utilitarian approach, a scorecard objectivecan be treated as a utility function expressing a decision maker'spreference over the domain values of a performance indicator.

For example, a scorecard objective such as “The overall service levelagreement (SLA) penalty cost should be less than $100000” expresses aconstraint over the domain values of the performance indicator “overallpenalty cost”. Any value above the target value ($100000) would not meetthe constraint while any value below would. In other words, theconstraint expressed in the scorecard objective partitions the set D ofdomain values of a performance indicator κ into two subsets, the subsetS containing the values that satisfy the constraint and the subset NScontaining the values that do not.

PROPOSITION 1. A scorecard objective expresses a decision maker'spreference over the domain values of the associated performanceindicator.

Because all the values contained in the S subset satisfy the constraint,from a decision maker point of view, they all yield that same degree ofsatisfaction. As long as the constraint is satisfied, any value of theperformance indicator is as good as the other. On the other hand, woulda decision maker be equally dissatisfied by the values in NS that do notsatisfy the constraint, or would a decision maker would prefer values ofthe performance indicator that are “close” to the objective than valuesthat are “far” from the objective.

Therefore, there exists a preference relation

o (“is preferred with regards to objective o”) over the set D of domainvalues of a performance indicator κ and that this preference isexpressed in reference to a target value in D and the constraintoperator (“greater than” or “lower than”) associated with the relatedobjective.

PROPOSITION 2. The preference relation

o can be represented by a von Neumann-Morgenstern utility function.

The preference relation

o is rational, that is:

-   -   (A.1)        o is complete, e.g., either p        o q or q        o p for all p, q ∈D    -   (A.2)        o is transitive, e.g., if p        o q and q        o r then p        o r for all p, q, r∈D

Given the properties of the preference relation

o, let φ_(o):D→[0,1] be a utility function representing the preferencerelation

o such that:

∀x, y∈D:x

_(o) y

φ _(o)(x)≧U ₀(y)   Equation 100

Based on the scorecard structure, mutual utility independence betweenthe utility functions representing the various objectives is assumed.

PROPOSITION 3. The utility function φ_(o)(.) representing the preferencerelationship expressed in the context of an objective o can be derivedfrom the objective's constraint operator, the target value and the riskattitude of the decision maker.

FIG. 2 describes a diagram illustrating a derivation process of autility function having a ‘greater than’ type objective, according to anembodiment. For ‘greater than’ operator, a utility function is riskaverse 210 if it is concave downward over the continuum in question. Itis risk seeking 230 if it is concave upwards over the continuum, and itis risk neutral 220 if it is linear over the continuum. The shaded area240 represents the values in the performance indicator space thatsatisfy the objective at any point in time. The derived utilityfunctions for a performance indicator values at a given time t, with tless than or equal to Evaluation time exhibit different risk postureswith regards to the ‘greater than operator’. Similarly, for a ‘lowerthan’ operator (not shown), a utility function is risk averse if it isconcave upwards over the continuum in question. It is risk seeking if itis concave downward over the continuum, and it is risk neutral if it islinear over the continuum. Various utility functions used may includehyperbolic absolute risk aversion (HARA) function, polynomial and splinefunctions.

PROPOSITION 4. The utility of a scorecard is calculated as a weightedsum of the objectives utility functions.

In a scorecard, objectives are clustered into perspectives (financial,customer, internal, and others). Relative importance of objectives in aperspective is determined by a weight with sum of the weights equal toone. Similarly, importance of the perspective in a scorecard is alsodetermined by a weight. To capture this, a utility function associatedwith an objective o in a perspective p is associated with a weight ω₀with:

ω₀=weight of objective o in perspective x weight of perspective p inscorecard with

${{\sum\limits_{i = 1}^{n}\omega_{oi}} = 1},$

the summation occurring for values of i from 1 to n. The utility of ascorecard s with n objectives is computed by Equation 200 as follows:

${\sigma (s)} = {\sum\limits_{i = 1}^{n}{\omega_{oi}{\phi_{oi}.}}}$

Impact of Business Decision Alternatives on Performance Indicators andBalanced Scorecards

FIG. 3 is a block diagram of a causality model 300 illustrating a causalrelationship between sets of an alternative, event, performanceindicator, objective and balanced scorecard, according to an embodiment.An alternative 310 selectable from a set of alternatives 312 results ina set of events 320 which in turn have specific consequences (oroutcomes) on a set of performance indicators 330. A change in the valuesof the set of performance indicators 330 affect the set of objectives340, which in turn affect the set of balanced scorecards 350. Additionaldetails of an exemplary representation of the causality model 300 usinga unified modeling language (UML) is described with reference to FIG. 6.

To illustrate the causality relationship, a scenario may exist in whicha decision maker may desire to prioritize Information Technology (IT)incidents and that Service Level Agreements (SLA's) have been defined onthe incident management process specifying specific times for thetreatment of such IT incidents. For instance, a gold SLA may specifythat incidents be treated within 4 hours of reception. A givenalternative would associate a priority to a specific incident resultingin an expected time of treatment. For example, a ‘High’ priority mayguarantee a time of treatment of 1 hour, plus or minus 15 minutes. Ifthe expected time of treatment is after the deadline computed form theSLA, the following event may be generated: violation of associatedservice level agreement (SLA). This event results in a unit increase forthe performance indicator measuring customer satisfaction and anincrease of the penalty cost associated with the SLA for the performanceindicator measuring the total penalty cost.

In this example, there is an uncertainty over the time (e.g., plus orminus 15 minutes) of treatment of the incidents. In other words, theconsequences of assigning a given priority to an incident results inuncertain consequences or outcomes. Thus, an alternative is equivalentto a set of simultaneous independent lotteries or prospects defined asprobability distributions over the domain values of the set ofperformance indicators 330. As described earlier, if Z is a finite setof consequences (or prizes or outcomes), then a lottery is a probabilitydistribution on Z.

Given a set of m alternatives included in the set of alternatives 312,

A _(i) ={L ^(i) ₁ , . . . , L _(n) ^(i)}  Equation 300

where A_(i), (1<i<m) is the i^(th) alternative and L^(i) _(j), (1<j<n)is the lottery on the j^(th) performance indicator for the i^(th)alternative. For discrete values of the performance indicator, theprobability density function is replaced with the probability massesrepresented by (p1, x1; . . . ; pn, xn) meaning that probability pj isassigned to outcome xj, for j=1, . . . , n. The probabilities pj arenonnegative and sum to one. Without loss of generality and forsimplification, the performance indicators are assumed to be discrete.To determine the optimum alternative, the solution defines a preferencestructure over the set of alternatives 312.

FIG. 4 is a graphical illustration of decision alternatives configuredas a set of lotteries, according to an embodiment. The decision makermay select any two alternatives A1 410 and A2 420 from the set ofalternatives 312 for comparison. The first alternative, A1 410, iscomposed of three concurrent lotteries respectively over theconsequences or outcomes {x,y,z}. The second alternative, A2 420, iscomposed of two concurrent lotteries over the consequences or attributes{x, z}. In order to select an optimum alternative between A1 410 and A2420, the decision maker establishes a preference between those twoalternatives. Since the outcomes of the two concurrent lotteries aredifferent, the preference between lotteries is restated or reformulatedin terms of preferences between probability distributions over the sameset of outcomes by homogenizing or adjusting the set of outcomesaccordingly. One such technique for homogenizing the set of outcomes isby using a degenerate lottery, which assigns a known probability of 1 ora 0 to a current value of an outcome.

Therefore, alternative A2 420, can be reformulated over the threeattributes {x, y, z} by introducing a degenerate lottery on y, which isa simple lottery that assigns probability 1 to the current value ofperformance indicator y, and 0 to all others. The two alternatives A1410 and A2 420 can now be compared after the homogenization process. Adecision making situation in which a decision maker or a decisionsupport system can assign mathematical probabilities to the randomnessis referred to as a situation under risk or an uncertain situation. Insuch a case, the behavior of the decision maker is fully defined by itspreferences on the probability distributions over the consequences ofthe alternatives. Therefore, the decision to select an alternative fromthe set of alternatives 312 is equivalent to defining a preferencerelation over a set of concurrent lotteries: {{L¹ ₁, . . . , L¹ _(n)}, .. . , {L^(m) ₁, . . . , L^(m) _(n)}}.

Preferences Over Concurrent Lotteries Under Risk

FIG. 5 is a flow chart of a method for decision making underuncertainty, according to an embodiment. In a particular embodiment, themethod is used to compare alternatives under risk, e.g., the set ofalternatives 312, based on the balanced scorecard 100. In order tocompare a set of concurrent lotteries, a preference relation over suchlotteries is established. To achieve this, the expected utility of asimple lottery over a performance indicator is assessed. Then, using theadditive properties of the utility functions derived from a scorecard,the expected utilities over each of the lotteries are aggregated. Theresult is the expected utility associated with that set of concurrentlotteries. Assuming that the preferences are in accordance with the vonNeumann-Morgenstern axioms, the preference relation over concurrentlotteries can be represented by the aggregation of the expectedutilities over simple lotteries.

A. Concurrent Lottery

DEFINITION 1. Let X be a set of variables. A k-concurrent lottery is aset of k (k=card(X)) simultaneous independent simple lotteries over eachelement of X.

DEFINITION 2. Let X be a set of variables and let Y, Z be two randomsubsets of X, with Y not equal to 0 and Z not equal to 0. Let Ly be aconcurrent lottery defined over Y and Lz be concurrent lottery definedover Z. L^(y) and L^(z) are homogeneous if, and only if, Y=Z.

DEFINITION 3. Let X be a set of variables and let x={x1, . . . , xn} bethe valuation of the variables in X at time t. Let Lx be an n-concurrentlottery over X at time t. The values in x are said to represent thestatus quo for Lx.

PROPOSITION 5. Let X be a set of variables and let Y, Z be two randomsubsets of X, with Y not equal to 0, Z not equal to 0 and Y not equal toZ. Let Ly be a concurrent lottery defined over Y and L^(z) be concurrentlottery defined over Z. L^(y) and L^(z) are homogenized by adding toL^(y) the degenerated lotteries on the status quo values of Z\Y and byadding to L^(z) the degenerated lotteries on the status quo values ofY\Z.

B. Expected Utility of a Simple Lottery Over a Performance Indicator

Based on the results described in the section entitled MODEL FORBALANCED SCORECARD, the expected utility (EU) for of a simple lottery Lover a performance indicator K is computed by equation 400 as follows:

$\begin{matrix}{{{EU}\left( L^{k} \right)} = {\sum\limits_{i = 1}^{n}{p_{i}{\phi_{ok}\left( x_{i} \right)}}}} & \left( {{Eq}.\mspace{14mu} 400} \right)\end{matrix}$

where φ_(ok)(.) is the utility function derived from objective o definedover performance indicator k as described in Equation 100. φ_(ok)(x_(i))is the utility of consequence or outcome x_(i) and p_(i) is theprobability associated with the outcome x_(i).

C. Expected Utility of Homogenous K-Concurrent Lotteries

PROPOSITION 6. Let X={x1, . . . , xn} be a set of discrete variables.Let L={L¹, . . . , L^(n)} be a set of lotteries defined over X whereeach Li is a simple lottery over variable x_(i). The expected utility ofL is computed by Equation 500 using Equation 400 as follows:

$\begin{matrix}{{{EU}(L)} = {\sum\limits_{i = 1}^{n}{{{EU}\left( L_{i} \right)}.}}} & \left( {{Eq}.\mspace{14mu} 500} \right)\end{matrix}$

The EU may also be computed if variables are associated with relativeimportance as performance indicators in the balanced scorecards.

PROPOSITION 7. Let X={x_(i), . . . , x_(n)} be a set of discretevariables and let Ω={ω₁, . . . , ω_(n)} be a set of weights where eachω_(i), (1<i<n) is the relative importance of the i^(th) variable in Xand sum of ω_(i)=1 (with i varying from 1 to n). Let L={L¹, . . . ,L^(n)} be a set of lotteries defined over X where each L^(i) is a simplelottery over variable x_(i). The expected utility of L is computed byEquation 600 as follows:

$\begin{matrix}{{{EU}(L)} = {\sum\limits_{i = 1}^{n}{\omega_{i}{{{EU}\left( L^{i} \right)}.}}}} & \left( {{Eq}.\mspace{14mu} 600} \right)\end{matrix}$

D. Preference Relation Homogenous K-Concurrent Lotteries

THEOREM 1. (Expected Utility Theorem) A preference relation

on the space of simple lotteries L satisfying the continuity andindependence axiom admits a utility representation of the expectedutility form such that for any two lotteries p, q belonging to L, thefollowing holds as described in Equation 700:

$\begin{matrix}\left. {p \succ q}\leftrightarrow{{\sum\limits_{x \in {{supp}{(x)}}}{u_{x}{p(x)}}} > {\sum\limits_{\notin {{supp}{(q)}}}{u_{x}{{q(x)}.}}}} \right. & \left( {{Eq}.\mspace{14mu} 700} \right)\end{matrix}$

That is, a lottery p is preferred to lottery q, if and only if, theexpected utility of p is greater than the expected utility of q.

THEOREM 2. Let L be space of simple lotteries defined over a set ofdiscrete variables. A preference relation

on the space of homogeneous k-concurrent lotteries C^(k) defined over Ladmits a utility representation of the expected utility form such thatfor any two lotteries k, I belonging to C^(k), the following holds asdescribed in Equation 800:

k

I⇄EU(k ^(i)) where k ^(i)∈ supp(k)>ΣEU(I ^(i)) where I^(i)∈ supp(l)  (Eq. 800)

where k^(i) denotes the i^(th) lottery in the concurrent lottery k andI^(i) denotes the i^(th) lottery in the concurrent lottery I. Theorem 2shows that the preference relationship over a set of a k-concurrentlottery can be represented by the expected utility function asdetermined in Proposition 7. Therefore, the utility functions used tocompare alternatives under uncertainty in light of balanced scorecardtake the expected utility form expressed in Proposition 7.

V. Method for Comparing Alternatives Under Risk Based on BalancedScorecard

The results on concurrent lotteries are integrated into a method forcomparing alternatives under risk, as illustrated in the flow chartdescribed with reference to FIG. 5. In a particular embodiment, themethod may be used to compare one or more alternatives from the set ofalternatives 312 by assessing the impact of these alternatives on theset of performance indicators 330, and hence on the set of balancedscorecards 350. Let K={κ1, . . . , κn} be a set of performanceindicators and let S be a scorecard defining objectives to be achievedover K.

At step 510, a causality framework that models the relationship betweenalternatives and consequences is provided. In a particular embodiment,the causality framework defines the relationships between an alternative(Ai) of the set of alternatives 312 and at least one performanceindicator of a set of performance indicators 330. Additional detail ofthe causality framework is described with reference to FIG. 6. At step520, a k-concurrent lottery (L^(i)) associated with the alternative (Ai)is conducted, the alternative (Ai) having consequences over k ones ofthe set of performance indicators. At step 530, the k-concurrent lottery(L^(i)) is homogenized (as described in Proposition 5) over the set ofperformance indicators if the k ones is less than a number of the set ofperformance indicators. At step 540, an expected utility of thek-concurrent lottery (L^(i)) for each one of the set of alternatives iscomputed as described in Proposition 7. At step 550, one alternative isselected from the set of alternatives 312, the selection occurring inaccordance with a selection criteria based on the expected utility. Theselection criteria may include selection functions such as a minimum, amaximum, greater than, less than, and other criteria. It is understoodthat various steps described above may be added, omitted, combined,altered, or performed in different orders.

Benefits of the tools and techniques for comparing alternatives underrisk described herein enable a decision maker to connect alternativeswith their impact on a balanced scorecard. For example, if a server goesdown and a decision maker needs to assess what alternative to opt forfrom a set of alternatives, e.g., repair it now, repair it tomorrow, orwait for the next maintenance cycle. The tools and techniques describedherein present the decision maker with the three alternatives along withtheir impact on the various objectives and performance indicators forassessment Repair now may have a positive impact on “up time” objectivebut may require allocating a specific resource, e.g., engineer beingallocated to another task, thereby increasing the cost associated withthis alternative, and thus having a negative impact of “cost ofdelivery” objective. Repair tomorrow may not be favorable to the “uptime” objective but may have a positive effect on the “cost of delivery”objective. Lastly, the wait for maintenance window alternative may notbe favorable to the “up time” objective but may be favorable to the“cost of delivery” objective. While selecting an alternative, the toolsand techniques described herein advantageously provide a declarative andanalytical framework to support the analysis and selection by providingclear consequences associated with the alternatives.

VI. An Open Model for Expressing Declaratively Casual RelationshipsBetween Events and Performance Indicators

FIG. 6 illustrates an exemplary representation of a causality model 300described with reference to FIG. 3 using a unified modeling language(UML), according to an embodiment. As described earlier, the causalitymodel 300 is described as being open because the framework provides fordifferent styles of consequences to be expressed through the concept ofa ‘modifier’. That is, a modifier is essentially a probabilitydistribution expressed over the range of the performance indicators orKPI's. Therefore, a consequence expresses how events are likely tomodify the values of KPI's. It is understood that the causality model300 may also be implemented using other tools and techniques, such asthe Resource Description Framework (RDF). The RDF may include extensionssuch as RDF Schema and languages such as the RDF Ontology Web Language(RDF/OWL).

The causality model 300 includes an EventInstance 690 module coupled toan EventType 680 module, a Consequence 610 module coupled to theEventType 680 module, a KPIType 620 coupled to the Consequence 610module, and the KPIType 620 module coupled to a KPlInstance 670 module.Relations between the coupled modules may be 1 to many (indicated by 1and *) or many to many (indicated by * and *). EventInstance 690 iscapable instantiating multiple instances of the event types. Each typeof the event that is instantiated is the EventType 680. The EventType680 may include multiple consequences, including a consequence 610. TheKPlInstance 670 is capable of generating an instance KPIType 620. Theconsequence 610 has a name 612, a description 614 and an IModifier 616,which is an interface that expresses how a consequence modifies theassociated performance indicator KPIType 620. Multiple ones of theconsequences may affect the same KPIType 620. If the KPIType 620 is ofdiscrete nature, then the IModifier 616 associated with the consequencewill be a discrete modifier. Alternatively, if the KPIType 620 is ofcontinuous nature, then the IModifier 616 associated with theconsequence will be a continuous modifier. A modifier is essentially aprobability distribution expressed over the range of the KPI.Consequences are associated with EventTypes. An EventInstance can havemultiple EventTypes. The EventType 680 and the KPIType 620 can havesuper-type and sub-type relationships.

FIG. 7 is a flow chart of a method for modeling consequences of eventson performance indicators, according to an embodiment. In a particularembodiment, the method may be used to model the consequences of the setof events 320 on the set of performance indicators 330. At step 710, acausality model is configured. The configuration of the causality modelincludes defining the events and defining the consequences associatedwith each one of the events. Each one of the consequences, theconsequences being associated with a particular event, defines how theparticular event is to modify a value of at least one of the performanceindicators associated with the particular event. At step 720, a processincluded in the causality model is configured, the process beingexecutable on a computer to determine an impact of the consequences onthe value. At step 730, a causality model management system isconfigured to manage the causality model. Additional detail of thecausality model management system is described with reference to FIG. 8.It is understood that various steps described above may be added,omitted, combined, altered, or performed in different orders.

FIG. 8 is a block diagram illustrating a causality model managementsystem 800, according to an embodiment. The causality model managementsystem 800 may be used to configure and operate the causality model usedfor modeling consequences of events on performance indicators. Thecausality model management system 800 includes a model repository 810 tostore instances of the causality model 300, a causality engine 820 toembody the algorithm, an interface 830 to communicate with othersystems, and a what-if engine 840 to simulate the consequencesassociated with selected ones of the events.

FIG. 9 illustrates a block diagram of a computer system 900, accordingto an embodiment. The computer system 900 includes a processor 910coupled to a memory 920. The memory 920 is operable to store programinstructions 930 that are executable by the processor 910 to perform oneor more functions. It should be understood that the term “computersystem” is intended to encompass any device having a processor that iscapable of executing program instructions from a memory medium. In aparticular embodiment, the various functions, processes, methods, andoperations described herein may be implemented using the computer system900. For example, the causality model 300, the balanced scorecard 100,the causality model management system 800 and similar others may beimplemented using the computer system 900.

The various functions, processes, methods, and operations performed orexecuted by the system 900 can be implemented as the programinstructions 930 (also referred to as software or simply programs) thatare executable by the processor 910 and various types of computerprocessors, controllers, central processing units, microprocessors,digital signal processors, state machines, programmable logic arrays,and the like. In an exemplary, non-depicted embodiment, the computersystem 900 may be networked (using wired or wireless networks) withother computer systems.

In various embodiments the program instructions 930 may be implementedin various ways, including procedure-based techniques, component-basedtechniques, object-oriented techniques, rule-based techniques, amongothers. The program instructions 930 can be stored on the memory 920 orany computer-readable medium for use by or in connection with anycomputer-related system or method. A computer-readable medium is anelectronic, magnetic, optical, or other physical device or means thatcan contain or store a computer program for use by or in connection witha computer-related system, method, process, or procedure. Programs canbe embodied in a computer-readable medium for use by or in connectionwith an instruction execution system, device, component, element, orapparatus, such as a system based on a computer or processor, or othersystem that can fetch instructions from an instruction memory or storageof any appropriate type. A computer-readable medium can be anystructure, device, component, product, or other means that can store,communicate, propagate, or transport the program for use by or inconnection with the instruction execution system, apparatus, or device.

The illustrative block diagrams and flow charts depict process steps orblocks that may represent modules, segments, or portions of code thatinclude one or more executable instructions for implementing specificlogical functions or steps in the process. Although the particularexamples illustrate specific process steps or acts, many alternativeimplementations are possible and commonly made by simple design choice.Acts and steps may be executed in different order from the specificdescription herein, based on considerations of function, purpose,conformance to standard, legacy structure, and the like.

Novel features believed characteristic of the present disclosure are setforth in the appended claims. The functionality of various modules,devices or components described herein may be implemented as hardware(including discrete components, integrated circuits andsystems-on-a-chip ‘SoC’), firmware (including application specificintegrated circuits and programmable chips) and/or software or acombination thereof, depending on the application requirements. Theaccompanying drawings may not to be drawn to scale and some features ofembodiments shown and described herein may be simplified or exaggeratedfor illustrating the principles, features, and advantages of thedisclosure.

While the present disclosure describes various embodiments, theseembodiments are to be understood as illustrative and do not limit theclaim scope. Many variations, modifications, additions and improvementsof the described embodiments are possible. For example, those havingordinary skill in the art will readily implement the steps necessary toprovide the structures and methods disclosed herein, and will understandthat the process parameters, materials, and dimensions are given by wayof example only. The parameters, materials, and dimensions can be variedto achieve the desired structure as well as modifications, which arewithin the scope of the claims. Variations and modifications of theembodiments disclosed herein may also be made while remaining within thescope of the following claims. For example, a few specific examples ofdata models are described. The illustrative system for decision makingunder uncertainty can be used with any suitable data models. Theillustrative techniques may be used with any suitable data processingconfiguration and with any suitable servers, computers, and devices. Inthe claims, unless otherwise indicated the article “a” is to refer to“one or more than one”.

1. A method for modeling consequences of events on performanceindicators, the method comprising: configuring a causality model, theconfiguring of the causality model includes defining the events anddefining the consequences associated with each one of the events, theconsequences associated with a particular event defines how theparticular event is to modify a value of at least one of the performanceindicators associated with the particular event; and configuring analgorithm included in the causality model, the algorithm is executableto compute an impact of the consequences on the value.
 2. The method ofclaim 1 further comprising: configuring a causality model managementsystem to manage the causality model, the causality model managementsystem includes a model repository to store instances of the causalitymodel, a causality engine to embody the algorithm, an interface tocommunicate with other systems, and a what-if engine to simulate theconsequences associated with selected ones of the events.
 3. The methodof claim 1, further comprising the causality model is an open model,wherein the open model provides the consequences to be expressed througha modifier.
 4. The method of claim 3, further comprising the modifier isa probability distribution expressed over a range of the performanceindicators.
 5. The method of claim 1, further comprising the algorithmincludes: a gathering of the consequences portion, wherein the gatheringof the consequences portion includes generating a consequence map foreach one of the events and associating the consequences with each one ofthe events; and a combining of the consequences portion, wherein thecombining of the consequences portion includes adding the consequencesdetermined by the consequence map to affect a particular performanceindicator.
 6. The method of claim 5, further comprising the combiningoccurs in accordance with a combination policy.
 7. The method of claim1, further comprising the causality model is capable of beingimplemented in one of a unified modeling language, a RDF Schema, andROF/OWL, or a combination thereof.
 8. A computer system for modelingconsequences of events on performance indicators, the computer systemcomprising: a computer processor; and logic instructions on tangiblecomputer readable media and executable by the computer processor, thelogic instructions being capable of: configuring a causality model, theconfiguring of the causality model includes defining the events anddefining the consequences associated with each one of the events,wherein the consequences associated with a particular event defines howthe particular event is to modify a value of at least one of theperformance indicators associated with the particular event; andconfiguring an algorithm included in the causality model, the algorithmis executable to compute an impact of the consequences on the value. 9.The computer system according to claim 8, the logic instructions arefurther capable of: configuring a causality model management system tomanage the causality model, the causality model management systemincludes a model repository to store instances of the causality model, acausality engine to embody the algorithm, an interface to communicatewith other systems, and a what-if engine to simulate the consequencesassociated with selected ones of the events.
 10. The computer systemaccording to claim 8, further comprising the causality model is an openmodel, and the open model provides the consequences to be expressedthrough a modifier.
 11. The computer system according to claim 10,further comprising the modifier is a probability distribution expressedover a range of the performance indicators.
 12. The computer systemaccording to claim 8, further comprising the logic instructions for thealgorithm include: a gathering of the consequences portion, wherein thegathering of the consequences portion includes generating a consequencemap for each one of the events and associating the consequences witheach one of the events; and a combining of the consequences portion,wherein the combining of the consequences portion includes adding theconsequences determined by the consequence map to affect a particularperformance indicator.
 13. The computer system according to claim 12,further comprising the combining occurs in accordance with a combinationpolicy.
 14. The computer system according to claim 8, further comprisingthe logic instructions for the causality model are capable of beingimplemented in one of a unified modeling language, a RDF Schema, andROF/OWL, or a combination thereof.
 15. A computer program product formodeling consequences of events on performance indicators, the computerprogram product embodied on a computer readable media, the computerprogram product comprising: logic instructions for configuring acausality model, the configuring of the causality model includesdefining the events and defining the consequences associated with eachone of the events, wherein the consequences associated with a particularevent defines how the particular event is to modify a value of at leastone of the performance indicators associated with the particular event;and logic instructions for configuring an algorithm included in thecausality model, the algorithm is executable to compute an impact of theconsequences on the value.
 16. The computer program product of claim 15further comprising: logic instructions for configuring a causality modelmanagement system to manage the causality model, the causality modelmanagement system includes a model repository to store instances of thecausality model, a causality engine to embody the algorithm, aninterface to communicate with other systems, and a what-if engine tosimulate the consequences associated with selected ones of the events.17. The computer program product of claim 15, further comprising thecausality model is an open model, wherein the open model provides theconsequences to be expressed through a modifier.
 18. The computerprogram product of claim 17, further comprising the modifier is aprobability distribution expressed over a range of the performanceindicators.
 19. The computer program product of claim 15, furthercomprising the logic instructions for the algorithm include: a gatheringof the consequences portion, wherein the gathering of the consequencesportion includes generating a consequence map for each one of the eventsand associating the consequences with each one of the events; and acombining of the consequences portion, wherein the combining of theconsequences portion includes adding the consequences determined by theconsequence map to affect a particular performance indicator.
 20. Thecomputer program product of claim 19, further comprising the combiningoccurs in accordance with a combination policy.